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Article

Symmetry Reduction and Numerical Solution of a Third-Order ODE from Thin Film Flow

by
E. Momoniat
* and
F.M. Mahomed
*
Centre for Differential Equations, Continuum Mechanics and Applications School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, South Africa
*
Authors to whom correspondence should be addressed.
Math. Comput. Appl. 2010, 15(4), 709-719; https://doi.org/10.3390/mca15040709
Published: 1 December 2010
Versions Notes

Abstract

A new approach to solving high-order ordinary differential equations numerically is presented. Instead of the usual approach of writing a high-order ordinary differential equation as a system of first-order ordinary differential equations, we write the high-order ordinary differential equation in terms of its differential invariants. The third-order ordinary differential equation y′′′ = y−k for constant k is used to illustrate this approach for the cases k = 2 and k = 3.
Keywords: Thin film; third-order ODE; symmetry reduction Thin film; third-order ODE; symmetry reduction

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MDPI and ACS Style

Momoniat, E.; Mahomed, F.M. Symmetry Reduction and Numerical Solution of a Third-Order ODE from Thin Film Flow. Math. Comput. Appl. 2010, 15, 709-719. https://doi.org/10.3390/mca15040709

AMA Style

Momoniat E, Mahomed FM. Symmetry Reduction and Numerical Solution of a Third-Order ODE from Thin Film Flow. Mathematical and Computational Applications. 2010; 15(4):709-719. https://doi.org/10.3390/mca15040709

Chicago/Turabian Style

Momoniat, E., and F.M. Mahomed. 2010. "Symmetry Reduction and Numerical Solution of a Third-Order ODE from Thin Film Flow" Mathematical and Computational Applications 15, no. 4: 709-719. https://doi.org/10.3390/mca15040709

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